Here is the full list of all 40 H-Rescue achievements.
Finish the first puzzle to unlock Hanna
Finish the first puzzle to unlock Ekio
Finish the first puzzle to unlock Ren
Finish the first puzzle to unlock Hikkata
Finish the first puzzle to unlock No'ou
Finish the first puzzle to unlock Izumi
Finish the first puzzle to unlock Amylia
Finish the first puzzle to unlock Tanya
Remove all magic on Hanna's body
Remove all magic on Ekio's body
Remove all magic on Ren's body
Remove all magic on Hikkata's body
Remove all magic on No'ou's body
Remove all magic on Izumi's body
Remove all magic on Amylia's body
Remove all magic on Tanya's body
Get the first combox4
Get combox4 3 times at any stage
Reach the end of game
Finish the first puzzle to unlock Hanna within 1 minute
Finish the first puzzle to unlock Ekio within 1 minute
Finish the first puzzle to unlock Hikkata within 1 minute
Finish the first puzzle to unlock Amylia within 1 minute
Complete remove all magic on Ekio's body without using any SHUFFLING
Complete remove all magic on Hikkata's body without using any SHUFFLING
Complete remove all magic on Amylia's body without using any SHUFFLING
Complete remove all magic on Tanya's body without using any SHUFFLING
Unlock all achievements
Save at least 5 girls at the end
Save all the girls at the end
Make a DIFFERENT choice
Finish the first puzzle to unlock Ren within 1 minute
Finish the first puzzle to unlock No'ou within 1 minute
Finish the first puzzle to unlock Izumi within 1 minute
Finish the first puzzle to unlock Tanya within 1 minute
Get 40.000 point at any stage
Complete remove all magic on Hanna's body without using any SHUFFLING
Complete remove all magic on No'ou's body without using any SHUFFLING
Complete remove all magic on Ren's body without using any SHUFFLING
Complete remove all magic on Izumi's body without using any SHUFFLING